NASA Technical Reports Server (NTRS) 19670021879: The composition of galactic cosmic rays

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THE COMPOSITION OF
GALACTIC COSMIC RAYS

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D.V. REAMES
C. E. FICHTEL

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JULY 1967

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GODDARD SPACE FLIGHT CENTER

GREENBELT MARYLAND

OG VI-47

The Composition of Galactic Cosmic Rays

D. V. Reames and C. E. Fichtel

NASA/Goddard Space Flight Center, Greenbelt, Maryland, U.S.A.

2

ABSTRACT

Recent measurements of low-energy galactic cosmic rays obtained on
sounding rockets and satellites exhibit a composition different from that
obtained for intermediate and high-energy radiation obtained at balloon
altitudes. In particular the ratio of light to medium nuclei is observed
to be 0.2 to 0.3 in the 50 to 100 MeV/nucleon interval as compared with
values near 0.5 in the 200 to 500 MeV/nucleon region. Lower values of
the ratios C/0, N/0, F/0 and odd-Z /eve n-Z are also found. In the light
of the:- •-! new measurements and of new measurements on the fragment tion
cross sections for cosmic-ray nuclei in interstellar space, an attempt
has been made to calculate the composition expected if similar source
spectra are assumed. It is founa that neither passage through a fixed
amount of material nor an equilibrium condition (exponential path length
distribution) is adequate to explain the observed features. The effects
of including other mechanisms such as rigidity-dependent escape from the
galaxy and Fermi acceleration in interstellar space are evaluated.

I Introduction

Virtually all of the quantitative theories contrived to explain
the energy-dependent composition of the galactic cosmic radiation
involve the propagation o t the radiation through interstellar material.

If this process occurs, at least two mechanisms must affect the cosmic-
ray composition and energy spectra; these are fragmentation produced in
nuclear reactions with the material (assumed to be mostly hydrogen) and
ionization energy loss. Additional processes which might affect the energy
dependence of the relative composition include Fermi- type, acceleration
in collisions of the cosmic-ray nuclei with magnetic irregularities

- 3 -

on clouds and rigidity dependent loss from the galaxy.

In this work we examine two extreme models of propagation process,
that in which the amount of interstellar material through which the
radiation propagates is constant, and the equilibrium model in which
supply of particles is balanced by their loss through the various
mechanisms mentioned above. These two models lead to delta-function
and exponential probability distributions for the path length
traversed , respectively.

The present re-examination of cosmic-ray propagation is occasioned
especially by the existence of new measurements on the fragmentation
cross sections which are, in some instances, quite different than those
previously assumed.

The assumptions made about the cosmic-ray source are that the spectrum
of all species emitted has the same shape and that the omitted fluxes of Li,
Be and B are negligible relative to Oxygen. Other abundances have been
treated as adjustable parameters.

Our calculations propagate individual elements from He through 0
and the charge groups 9 £ Z £ 19 and Z > 20. Having obtained the
abundances of the individual species at earth as a function of energy/
nucleon we sum to find the energy-dependent ratio of Light ( 3 £ Z £ 5)
to Medium (6 £ Z £ S) nuclei. We make the approximation that the
charge to mass ratio of all species considered is %.

II Theory

The theory of energy-dependent propagation of cosmic-rays through
interstellar space has been described recently by Fichtel and Reames (1966).
The transport equation used in that work is

( 1 )

- 4 -

3 x I w i (E) Ji (E,X )1 +wi (E) j t (E,X)/A i (E)=Z_j k (E,X)/A ki (E)

k>i

where (E,X) is the flux per unit energy /nucleon of i-type particles
of energy/nucleon E after propagation through X g/cm 2 of material,
and (E) = dE/dx for these particles.

For the equilibrium case we begin with the equation of Ginzburg and
Syrovatskii (1964) for the general energy-dependent number density of i-type
cosmic rays which we write as

:)Ni

A

( 2 )

l-i - A.( Di A Ni ) + ~L (b . Ni ) - j

1 .} 3

AE

(dl.NO

=Qi- N t /Ti + k> . N k /T ki

Since we are concerned with the equilibrium case lN/At = 0. We also
assume that there are no spatial variations or second order energy
effects so that the second and fourth terms in (2) are zero.

To write Eq (2) in terms of fluxes and convert t to x we let
~ PNi, b- = dE/dt ~ pdE/dx = gw^E), and Aj_ ~ Bt^, since
dx = ppcdt ~ pdt. With these substitutions Eq. (2) becomes

(3) [w ± (E) Ji (E)] + Ji (E)/Ai (E) = Qi (E) + 2 (E)/A kl (E)

It is easy to show that the solutions of Eq (1) and (3) are
related by

(4) J ± (E) = ji (E,X)dx

and that

(5)

Qi (E) - Ji (E,0)

5

where the integral in Eq. (4) runs over all X for cons tant E. It is
thus possible to obtain equilibrium solutions by integrating
those obtained for differing amounts of material, i.e. over increasingly
"older 11 spectra at constant energy.

In addition to the ionization energy loss we have investigated
the effect of including a small amount of Fermi acceleration (Fermi, 1949,
1954). This acceleration has been included directly in the dE/dx
term, i.e.

= dE/dx (ionization) + aW

^ =- ii- £(g) + OW

M i

where W is the total energy /nucleon.

In Eq. (6) a has been chosen in the range 0 to 0.03 ctrf*/g. These
values are several orders of magnitude smaller than that necessary to
produce the observed slope of the particle spectra with this acceleration
alone, and are more nearly in accord with values estimated from
measurements on magnetic clouds in interstellar space.

The final effect included is a rigidity-dependent escape from the
galaxy using the equilibrium model. Actually an escape of this kind
should be included as a boundary condition on Eq. (2), since it will,
in general, couple energy and spatial dependences. Following the
example of Cowsik et al. (1966), however, we have included this effect
as a volume loss term A g = K/R, normalized to 3 g/cm 3 at 8 GV.

Ill Fragmentation Cross Sections

Our previous work (Fichtel and Reames 1966) did not account for a

6

number of new measurements on the fragmentation of nuclei in proton
reactions. Significant among these is the first measurement of the
production of the stable isotopes Li e and Li 1 in proton reactions with
C 12 and 0 16 (Bemas et al., 1965). Other data not included in older
summaries have been measured for C 13 (p,x) Be 7 (Williams and Fulmer,
1967), and for production of 0 16 , N 13 , C 11 and Be 7 in 0 16 (p,x)
reactions (Albouy et al., 1962). Recent summaries of measurements
have also been made (Bertini et al., 1966 and Bemas et al., 1967).

From these measurements and from the theoretial work of Bertini
et al and Bernas et al we have attempted to better estimate the
fragmentation cross sections, the results for the production of Li
and B from various species are shown in Fig. 1.

It is interesting to note that the high-energy cross section for
the production of stable Li isotopes from C 13 (p,x) reactions is
almost a factor of two lower than that estimated previously
(Badhwar et al., 1962). This result is not entirely surprising since
the previous result was based on measurements from neutron bombardment,
these being the only data available at that time. Differences in
the results from p and n reactions on the same target leading to
the same product are expected (Bernas et al., 1967). No violation
in isotopic spin conservation need be involved to produce such
d if ferences .

Errors in the final Li abundance from errors in the cross sections
probably do not exceed 25%. In the case of boron production. Fig. 1
shows that most of the B results from fragmentation of carbon and in
fact comes from the C 13 (p,pn) C 11 (P + v) B 11 reaction and decay. Since
the more-poorly-known reactions contribute less to the total boron
production, the error in the latter is probably also not more than
20 to 30%.

7

IV Results and Discussion

The resultant L/M ratio calculated using the two different models
and various mechamisms described are shown with the data in Fig. 2.

Data are taken from the summary of Fichtel and Reames (1967). Clearly
no striking agreement exists between the theory and the measurements.

Most of the previous agreement has been destroyed by the use of
the new cross-section measurements. The dominant cross sections are
flat or rising with energy in the same energy region where the
L/M ratio appears to be reaching a maximum and then decreasing with
energy.

The inclusion of Fermi acceleration (or/0) generally affects the
L/M ratio at low energies. Effects associated with the crossover from
acceleration to deceleration (occurring at different E for different
species) are too weak to be observed.

Equilibrium spectra fail to explain the data unless a rigidity-
dependent loss from the galaxy is assumed. We are somewhat reluctant
to accept such a loss mechanism for a number of reasons. First, the
L/M ratio predicted decreases at high energies in proportion to the
loss term (eg. like K/R) , apparently no such effect is observed.

Second, the high-energy spectrum emitted by the source must be flatter
with energy for losses as strong as R” 1 ; if the observed spectrum goes
as R~ 2 ’ 6 the source spectrum must go as R” 1 * 5 to account for a K/R loss.
This means that the source must emit many orders of magnitude more
energy in cosmic-rays than previously believed.

In all the results plotted in Fig. 2 we have used a differential
rigidity spectrum proportional to R~ 3 * 6 except in the case of the
equilibrium spectrum with the K/R loss described above. Numerous
other spectral shapes have been used in our calculations, but give equally

poor agreement.

- 8 -

The general inadequacy of the present theories may arise from any
of several sources: 1) Propagation through interstellar space may not
be the dominant process for producing light nuclei and/or they may be
emitted directly by the source, 2) The cross sections used here may
not be appropriate, cross sections for processes other than p + C 12
or p + 0 ife5 may dominate the production of light nuclei, 3) The observed
features of the galaxy are considerably more complicated than expressed in
either of the models considered here; the path length distribution
might be a more complicated function of X and E. We tried to avoid
treating the path length as totally phenominological parameter.

In view of the poor agreement of the theories with the L/M data
we do not present other ratios which have been calculated on this
individual-element abundances obtained from the theories.

REFERENCES

G. Albouy, J. P. Cohen, M. Gusakow, N. Poffe, H. Sergolle and
L. Valentin, Physics Letters 2 , 306 (1962).

G. D. Badhwar, R. R. Daniel and B. Vijayalakshmi, Progr. Theoret.
Phys. 30, 607 (1962).

R. Bernas, M. Epherre, E. Gradsztajn, R. Klapisch and F. Yiou,
Physics Letters ^5,, 147 (1965).

R. Bernas, E. Gradsztajn, H. Reeves and E. Schatzman, Ann. of
Phys. (to be published, 1967).

H. w. Bertini, M. P. Guthrjej E. H. Pitkell and B. L. Bishop, Oak
Ridge National Laboratory Report 0RNL-3884 (1966).

R. Cowsik, Yash Pal, S. N. Tandon and R. P. Verma, Tata Institute
of Fundamental Research report N.E. 66-18 (1966).

E. Fermi, Phys. Rev. 7_5, 1169 (1949).

E. Fermi, Astrophys. J. 119 , 1 (1954).

C. E. Fichtel and D. V. Reames, Phys. Rev. 149 , 995 (1966).

C. E. Fichtel and D. 'V. Reames, Phys. Rev. (to be published, 1967).

V. L. Ginzburg and S. I. Syrova tskii. The Origin of Cosmic Rays
(MacMillan Co., New York, 1964).

I. R. Williams and C. B. Fulmer, Phys. Rev. 154 . 1005 (1967)

60

cr (mb)

PROTON ENERGY (MEV)

Figure 1

080

Figure 2

ENERGY